*6. Consider the following LP:

Maximize z = XI + 5X2 + 3X3 subject to XI + 2X2 + X3 = 3 2xI - X2 = 4 Xl, X2, X3 ;::: 0 164 Chapter 4 Duality and Post-Optimal Analysis The starting solution consists of x) in the first constraint and an artificial X4 in the second constraint with M = 100. The optimal tableau is given as Basic Xl X2 X3 X4 Solution z 0 2 0 99 5

.1:3 1 2.5 1 -.5 1 x, 0 -.5 0 .5 2 4.2 Write the associated dual problem and determine its optimal solution in two ways.